Bernoulli Equation

In an ideal inviscid, incompressible flow, we have, by conservation of energy,

$\displaystyle p + \frac{1}{2}\rho u^2 + \rho g h =$   constant

where

\begin{eqnarray*}
p &=& \mbox{pressure (newtons/m$^2$\ = kg /(m s$^2$))}\\
u &=...
...\
\mbox{\lq\lq Inviscid''} &=& \mbox{\lq\lq Frictionless'', \lq\lq Lossless''}
\end{eqnarray*}

This basic energy conservation law was published in 1738 by Daniel Bernoulli in his classic work Hydrodynamica.

From §B.7.3, we have that the pressure of a gas is proportional to the average kinetic energy of the molecules making up the gas. Therefore, when a gas flows at a constant height $ h$, some of its ``pressure kinetic energy'' must be given to the kinetic energy of the flow as a whole. If the mean height of the flow changes, then kinetic energy trades with potential energy as well.


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Bernoulli Effect
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Pressure is Confined Kinetic Energy